O.K. I was a wee bit confused about Mauer/Varitek because Mauer is listed both as Vs. RHP and in the bench. Its a really good tandem there. I agree with you, I think I'd rather have Mauer starting vs RHP and then switching if needed.
My only ? is with Mueller. I think he IS the best option you have for 3B but his gbAs are a bit funky for my taste . I looked through your 3 franchises but I don't see many options though. Carroll poped in my mind vs. LHP. But, I'd probably go with him as well.
I have a franchise-themed team at the mo where one team is Minn. I ended up choosing Redmond over Mauer mostly for his positive clutch and because he can use my park better than Mauer, but in any other time I would choose Mauer's stronger arm, lower gbAs and better speed. And especially with your franchises I'd go with Mauer. Nice team Lucky. 8)